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(B) Let the fraction be $\frac{x}{y}$.According to the problem,the difference between the numerator and denominator is $5$,so $x - y = 5$,which implie

Vedclass · Accepted Answer

$2\frac{1}{4}$

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(B) Let the fraction be $\frac{x}{y}$.According to the problem,the difference between the numerator and denominator is $5$,so $x - y = 5$,which implies $x = y + 5$.When $5$ is added to the denominator,the new fraction becomes $\frac{x}{y+5}$.Given that the fraction decreases by $1 \frac{1}{4} = \frac{5}{4}$,we have:$\frac{x}{y} - \frac{x}{y+5} = \frac{5}{4}$.Substitute $x = y + 5$ into the equation:$\frac{y+5}{y} - \frac{y+5}{y+5} = \frac{5}{4}$$\frac{y+5}{y} - 1 = \frac{5}{4}$$\frac{y+5}{y} = 1 + \frac{5}{4} = \frac{9}{4}$$4(y+5) = 9y$$4y + 20 = 9y$$5y = 20 \Rightarrow y = 4$.Since $x = y + 5$,we have $x = 4 + 5 = 9$.The fraction is $\frac{x}{y} = \frac{9}{4} = 2 \frac{1}{4}$.

The difference between the numerator and the denominator of a fraction is $5$. If $5$ is added to its denominator,the fraction is decreased by $1 \frac{1}{4}$. Find the value of the fraction.

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